Abstract
This paper is devoted to the presentation of an efficient algorithm for interpolating with Simplicial Polynomial Finite Elements. We present first some general results on the construction of piecewise polynomial interpolation of class Ck on a triangulated domain in IRd. Then, we lay emphasis on triangular C1 and C2 elements, and show that the proposed algorithm is efficient, especially for the computation of surfaces interpolating scattered data.
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References
Argyris, J.H., Fried, I., and D.W. Scharpf, The TUBA family of plate elements for the matrix displacement method, J. Royal Aeronautic Society 72 (1968), 701–709.
Bell, K., A refined triangular plate bending element, Internat. J. Numer. Methods Engrg. 1 (1969), 101–122.
Bernadou, M. and J.M. Boisserie, The Finite Element Method in Thin Shell Theory, Birkhäuser-Verlag, Basel, 1982.
Chui, C.K. and M.J. Lai, On bivariate vertex splines, in Multivariate Approximation Theory III, W. Schempp and K. Zeller (Eds.), ISNM 75, Birkhäuser-Verlag, Basel, 1985, 84–102.
Ciariet, P.G., The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978.
Correc, Y. and E. Chapuis, Fast computation of Delaunay triangulation, Advances in Engineering Software 9 (2) (1987), 77–83.
Dyn, N. and D. Levin, Iterative solution of systems originating from integral equations and surface interpolation, SIAM J. Numer. Anal. 20 (1983), 377–390.
Duchon, J., Interpolation des fonctions de deux variables suivant le principe de la flexion des plaques minces, RAIRO Model. Math. Anal. Numér. 10 (1976), 5–12.
Lafranche, Y., Application de l’interpolation polynomiale au dépouillement graphique de valeurs dans IR, Thèse, 3ème cycle, Université de Rennes, 1984.
Le Méhauté, A.J.Y., Taylor interpolation of order n at the vertices of a triangle. Applications for Hermite interpolation and finite elements, in Approximation Theory and Applications, Z. Ziegler (Ed.), Academic Press, New York, 1981, 171–185.
Le Méhauté, A.J.Y., Interpolation et approximation par des fonctions polynomiales par morceaux dans JRn, Thèse d’Etat, Université de Rennes, 1984.
Le Méhauté, A.J.Y., An efficient algorithm for Ck-simplicial finite element interpolation in IRn, Annex, CAT Report #111, Texas A&M University, College Station, March 1986.
Morgan, J. and R. Scott, A nodal basis for C 1 piecewise polynomials of degree ≥ 5, Math. Comp. 29 (1975), 736–740.
Paihua, L., Méthodes numériques pour l’obtention de fonctions splines de type plaque mince en dimension 2, Séminaire d’Analyse Numérique, Rapport 273, Université de Grenoble, 1977.
Schumaker, L.L., Numerical aspects of spaces of piecewise polynomials on triangulation, CAT Report # 91, Texas A&M University, College Station, October 1985.
Ženišek, A., A general theorem on triangular C n elements, RAIRO Modél. Math. Anal. Numér. 4 (1974), 119–127.
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Le Méhauté, A. (1990). An Efficient Algorithm for C k Simplicial Finite Element Interpolation in IRd . In: Haußmann, W., Jetter, K. (eds) Multivariate Approximation and Interpolation. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 94. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5685-0_13
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DOI: https://doi.org/10.1007/978-3-0348-5685-0_13
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-5686-7
Online ISBN: 978-3-0348-5685-0
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